Alfreton Town have a six point cushion to safety after they were beaten 2-0 by Grimsby Town on Easter Monday.
Their cause was helped after fellow strugglers Dartford, Welling United and Nuneaton Town also failed to win.
It was always going to be a tough task for the Reds against a Mariners side bidding for promotion back to the Football League, that difficulty compounded by the 2,500 travelling fans who boosted the bumper Bank Holiday crowd to 3327 - just 27 short of the gate against Mansfield Town in February 2012.
Lenell John-Lewis squandered the first chance of the game in the fifth minute after Callum Howe’s back pass had sold Tom Flynn short.
Dan Bradley fired well wide from 25 yards two minutes later for Alfreton, then Flynn blocked another John-Lewis effort from a Jack Mackreth pass before Craig Clay’s shot from 20 yards was gathered at the second attempt by Flynn.
Craig Disley went close for the visitors with an 18th minute header, then five minutes after that Jimmy Phillips set up a clear chance for the Reds with Karl Hawley controlling his cross with a header before flicking the ball wide from close range.
A promising move involving Tom Shaw, Hawley and Phillips led to Jake Speight miscuing on the right edge of the area in the 26th minute, then Christian Jolley’s crossfield pass intended for Mackreth was accurately intercepted by Anthony Howell.
John-Lewis dragged another opportunity wide, Shaw almost succeeded from a free-kick just outside the area in response, then John-Lewis had a 20 yarder held by Flynn.
Phillips fired wide from 18 yards as the second half began, then a driven cross by Mackreth was guided back to his keeper by Luke Graham under pressure, the Reds then breaking swiftly with Speight curling a shot beyond the back post.
Bradley Wood had to be alert as John-Lewis sent Mackreth on a 54th minute run, then John-Lewis failed again from the edge of the area.
Gregor Robertson looked certain to score after a menacing run that needed a goal-line clearance from Bradley on 62 minutes, but seven minutes later the deadlock was broken when Mackreth’s shot following a partially cleared corner was diverted out of Flynn’s reach by Grimsby defender Josh Gowling.
Andi Thanoj sent a 71st minute free-kick whistling inches wide, but two minutes later Mackreth shot against the foot of the post from 12 yards, then Phillips lofted a half-chance over for Alfreton.
An equaliser looked imminent with 11 minutes remaining as Hawley tried to scoop the ball over the line after Graham had nodded down a Wood free-kick, but the ball rebounded off the underside of the crossbar for Gowling to hack clear.
A penetrating run by John Johnston was halted by Shaun Pearson’s timely tackle, but John-Lewis finally found the net with a downward header from Clay’s 87th minute cross to settle the outcome.
ALFRETON: Flynn; Wood, Graham, Howe, Rowe-Turner, Speight, Bradley, Shaw (Thanoj 66 mins), Howell (lronside 84 mins), Phillips (Johnston 78 mins), Hawley.
Subs not used: Courtney, Lenighan.